年龄别生育率建模和预测的最佳Box-Cox转换参数的选择
Selection of the optimal Box-Cox transformation parameter for modelling and forecasting age-specific fertility
摘要：
Box-Cox变换有时可以在模型简单性、方差齐性和估计精度方面产生显著的改进，例如在建模和预测特定年龄生育率方面。尽管其重要性，有很少的研究集中在人口预测的Box-Cox转换参数的最佳选择。提出了一种选择最优Box-Cox变换参数的简单方法，以及基于样本预测误差度量的算法。以澳大利亚特定年龄生育率为例，选择Box-Cox变换参数可以提高预测方法的样本外精度。此外，对数转换不足以建模和预测特定年龄的生育率。Box-Cox转换参数应嵌入特定年龄人口统计数据的统计分析中，以充分捕捉预测的不确定性。
英文摘要：
The Box-Cox transformation can sometimes yield noticeable improvements in model simplicity, variance homogeneity and precision of estimation, such as in modelling and forecasting age-specific fertility. Despite its importance, there have been few studies focusing on the optimal selection of Box-Cox transformation parameters in demographic forecasting. A simple method is proposed for selecting the optimal Box-Cox transformation parameter, along with an algorithm based on an in-sample forecast error measure. Illustrated by Australian age-specific fertility, the out-of-sample accuracy of a forecasting method can be improved with the selected Box-Cox transformation parameter. Furthermore, the log transformation is not adequate for modelling and forecasting age-specific fertility. The Box-Cox transformation parameter should be embedded in statistical analysis of age-specific demographic data, in order to fully capture forecast uncertainties.
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